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@Assessing Teaching PracticePractice
@Assessing Teaching PracticePractice
The research reported here was supported by the National Science Foundation, through a grant to the University of Michigan. The opinions, findings, and recommendations expressed are those of the authors and do not represent views of the National Science Foundation.
CONNECTING MATHEMATICAL KNOWLEDGE AND DISPOSITIONS
WITH PEDAGOGICAL SKILLS
Meghan Shaughnessy & Timothy BoerstNCTM Research Conference • San Diego, CA • April 2, 2019
Acknowledging our colleagues on this study: Merrie Blunk, Rosalie DeFino, Erin Pfaff, Xueying Ji Prawat, & Emily Theriault-Kimmey
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OUR GOAL FOR MATHEMATICS TEACHER EDUCATION: WELL-STARTED BEGINNERS
Preparing elementary teachers of mathematics who are ready for responsible professional work with students from the day they assume responsibility for classrooms of their own through learning experiences that integrate and advance:§ Mathematical Knowledge for Teaching (MKT)§ Productive mathematical dispositions § Skill with essential teaching practices
… all with room (and tools!) for further growth and development
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The field acknowledges that mathematical knowledge and mathematical dispositions impact teaching, but how and in what way?
How are teachers’ eliciting and/or interpreting of a student thinking impacted by their mathematical knowledge and/or dispositions?
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§ Participants: 24 preservice teachers, range of points in the teacher education program
§ Data Collection Part 1:§ Measure of knowledge of four specific subtraction approaches§ Measure of disposition towards four subtraction approaches
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AN EXAMPLE: STUDENT APPROACHES TO SUBTRACTIONShowing mathematical knowledge though:§ Describing the steps of the
process and their sequence§ Justifying and generalizing§ Applying the approach to
another problem
Showing mathematical dispositions toward the process through responses to questions:§ Is the approach sensible?§ Would you use the process yourself?
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STUDYING THE CONNECTION OF MKT, DISPOSITION, AND TEACHING PRACTICESimulations are approximations of practice that can be used to study the connections among MKT, disposition, and teaching practice.Simulations:§ are commonly used in many professional fields§ place authentic, practice-based demands on a participant § purposefully suspend or standardize some elements of the
practice-based situation § can provide insights that are not possible or practical to
determine in real-life professional contexts
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§ Participants: 24 preservice teachers, range of points in the teacher education program
§ Data Collection Part 1:§ Measure of knowledge of four specific subtraction approaches§ Measure of disposition towards four subtraction approaches
§ Data Collection Part 2:§ Three simulation assessments, including:
§ one that was high preference/high mathematical knowledge § one that was low preference/low mathematical knowledge§ one that was low preference/high mathematical knowledge
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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License https://creativecommons.org/licenses/by-nc-nd/4.0/
The preservice teacher1. Prepares for an interaction with a standardized student
about one piece of student work2. Interacts with the “student” to elicit the student’s thinking 3. Interprets the student’s thinking in a follow up interview,
using evidence from the interaction
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Strong math knowledge & Positive dispositionWeak math knowledge & Negative dispositionStrong math knowledge & Negative disposition
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Eliciting the student’s understanding was stronger in a strong math knowledge/positive disposition situation compared to a weak math knowledge/negative disposition situation
ELICITING OF THE STUDENT’S UNDERSTANDING
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0
0.2
0.4
0.6
0.8
1
Mea
n Ov
erall
Sco
re
Strong math knowledge & Positive dispositionWeak math knowledge & Negative dispositionStrong math knowledge & Negative disposition
p < .001
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Does mathematics knowledge matter when disposition is about the same?Eliciting the student’s understanding was stronger when math knowledge was strong compared to a weak math knowledge situation
ELICITING OF THE STUDENT’S UNDERSTANDING
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0
0.2
0.4
0.6
0.8
1
Mea
n Ov
erall
Sco
re
Strong math knowledge & Positive dispositionWeak math knowledge & Negative dispositionStrong math knowledge & Negative disposition
p = .032
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Does disposition matter when math knowledge is about the same? Eliciting the student’s understanding was stronger in a positive disposition situation compared to a negative disposition situation (marginally significant)
ELICITING OF THE STUDENT’S UNDERSTANDING
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0
0.2
0.4
0.6
0.8
1
Mea
n Ov
erall
Sco
re
Strong math knowledge & Positive dispositionWeak math knowledge & Negative dispositionStrong math knowledge & Negative disposition
p = .059
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Stronger knowledge of the mathematics of the algorithm and having a positive disposition towards the algorithm (relative to other algorithms) both had a positive impact on eliciting the student’s understanding.
0
0.2
0.4
0.6
0.8
1
Mea
n Ov
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Sco
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Strong math knowledge & Positive dispositionWeak math knowledge & Negative dispositionStrong math knowledge & Negative disposition
p < .001 p = .059p = .032
ELICITING OF THE STUDENT’S UNDERSTANDING
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Stronger knowledge of the mathematics of the algorithm and having a positive disposition towards the algorithm (relative to other algorithms) both had a positive impact on eliciting the student’s understanding.
0
0.2
0.4
0.6
0.8
1
Mea
n Ov
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Sco
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Strong math knowledge & Positive dispositionWeak math knowledge & Negative dispositionStrong math knowledge & Negative disposition
p < .001 p = .059p = .032Why? Mathematical knowledge of the
algorithm may support PSTs in identifying understandings to ask about (and in posing a question focused on that understanding)
Why? Positive disposition towards the algorithm may result in PSTs knowing
that the algorithm is understandable and that there are questions to ask about it
ELICITING OF THE STUDENT’S UNDERSTANDING
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INTERPRETING THE STUDENT’SUNDERSTANDING (OPEN ENDED)Interpreting the student’s understanding was stronger in a strong math knowledge/positive disposition situation compared to a weak math knowledge/negative disposition situation
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0
0.2
0.4
0.6
0.8
1
Mea
n Ov
erall
Sco
re
Strong math knowledge & Positive dispositionWeak math knowledge & Negative dispositionStrong math knowledge and Negative disposition
p = .002
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INTERPRETING THE STUDENT’S UNDERSTANDING (OPEN ENDED)Does mathematics knowledge matter when disposition is about the same?Interpreting the student’s understanding was stronger when math knowledge was strong compared to a weak math knowledge situation
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0
0.2
0.4
0.6
0.8
1
Mea
n Ov
erall
Sco
re
Strong math knowledge & Positive dispositionWeak math knowledge & Negative dispositionStrong math knowledge and Negative disposition
p < .001
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INTERPRETING THE STUDENT’S UNDERSTANDING (OPEN ENDED)Does disposition matter when math knowledge is about the same? Disposition did not appear to impact interpreting the student’s understanding
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0
0.2
0.4
0.6
0.8
1
Mea
n Ov
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Sco
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Strong math knowledge & Positive dispositionWeak math knowledge & Negative dispositionStrong math knowledge and Negative disposition
No significant difference
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INTERPRETING THE STUDENT’S UNDERSTANDING (OPEN ENDED)Stronger knowledge of the mathematics of the algorithm relative to other algorithms had a positive impact on interpreting the student’s understanding. Disposition did not appear to impact.
0
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1
Mea
n Ov
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Sco
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Strong math knowledge & Positive dispositionWeak math knowledge & Negative dispositionStrong math knowledge & Negative disposition
p = .002 p < .001 No significant difference
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INTERPRETING THE STUDENT’S UNDERSTANDING (OPEN ENDED)Stronger knowledge of the mathematics of the algorithm relative to other algorithms had a positive impact on interpreting the student’s understanding. Disposition did not appear to impact.
0
0.2
0.4
0.6
0.8
1
Mea
n Ov
erall
Sco
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Strong math knowledge & Positive dispositionWeak math knowledge & Negative dispositionStrong math knowledge & Negative disposition
p = .002 p < .001 No significant difference
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Why? Mathematical knowledge of the algorithm may support PSTs in identifying understandings to make inferences about and in making sense of evidence gathered
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INTERPRETING THE STUDENT’S UNDERSTANDING (PREDETERMINED)
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p = .016 No significant difference p = .030
Positive disposition towards the algorithm relative to other algorithms had a positive impact on interpreting the student’s understanding of a specific idea. Mathematical knowledge did not appear to impact.
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1
Mea
n Ov
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Sco
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Strong math knowledge & Positive dispositionWeak math knowledge & Negative dispositionStrong math knowledge & Negative disposition
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INTERPRETING THE STUDENT’S UNDERSTANDING (PREDETERMINED)
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p = .016 No significant difference p = .030
Positive disposition towards the algorithm relative to other algorithms had a positive impact on interpreting the student’s understanding of a specific idea. Mathematical knowledge did not appear to impact.
0
0.2
0.4
0.6
0.8
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Mea
n Ov
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Sco
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Strong math knowledge & Positive dispositionWeak math knowledge & Negative dispositionStrong math knowledge & Negative disposition
Why? Positive disposition towards the algorithm may support PSTs in trusting/not discounting the
understandings conveyed about the approach
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§ What are some possible explanations for the findings… § Eliciting and interpreting process: not markedly impacted by
differences in knowledge or disposition.§ Eliciting understanding: impacted by differences in knowledge
and disposition.§ Interpreting understanding (open ended): impacted by
differences in knowledge, but not disposition§ Interpreting understanding (predetermined): impacted by
differences in disposition, but not knowledge
§ What are some implications of these findings for TE?
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QUESTIONS? WANT MORE INFORMATION?http://sites.soe.umich.edu/at-practice/
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